Problem: Solve for $x$ and $y$ using elimination. ${-2x-5y = -29}$ ${2x-6y = -4}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-11y = -33$ $\dfrac{-11y}{{-11}} = \dfrac{-33}{{-11}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {-2x-5y = -29}\thinspace$ to find $x$ ${-2x - 5}{(3)}{= -29}$ $-2x-15 = -29$ $-2x-15{+15} = -29{+15}$ $-2x = -14$ $\dfrac{-2x}{{-2}} = \dfrac{-14}{{-2}}$ ${x = 7}$ You can also plug ${y = 3}$ into $\thinspace {2x-6y = -4}\thinspace$ and get the same answer for $x$ : ${2x - 6}{(3)}{= -4}$ ${x = 7}$